Multi-scale Modeling for Life-Cycle Management of Concrete Structures

Underground space fatigue failure of RC bridge deck

Koichi Maekawa T. Ishida

Y. Hiratsuka X. Zhu

(1) Summary of multi-scale platform

(2) Seismic response of multi-story RC building and impact

of drying (weak coupling)

(3) Long-term deformation of underground RC culverts and

durability over 30 years (weak coupling)

(4) Fatigue life assessment of bridge decks (strong coupling)

(5) PDCA cycle for asset management

Building management against earthquake and aging

Concrete

Aggregate, cement paste matrix, interfacial transition zone

Capillary water, C-S-H hydrate

Gel pores, water molecule, C-S-H layer structure

cm

mm

m

nm

Size

Reinforced Concrete

m

Time (Days) 10-1 100 101 104 102 103

Construction In service Deterioration Curing

105 106 107

Long-term Durability

Shrinkage & Thermal cracking

Long-term deflection of PC bridge

Nuclear waste barrier facility Ultra long-term stability

Fatigue of RC slab

Shear failure of column

Multi-scale modeling and simulation with regard to the space and the time domains

Carbonation, Chloride Rebar Corrosion

km

Inner hydrate Outer hydrate Interlayer 2.8 thick

Gel pore II (1.6nm~) Pore among gel grain

Gel pore I (~1.6nm) Pore inside gel grain

Capillary pore Free space for hydrate

Unhydrated cement

Hydrate product (C-S-H grain)

Low hydration

After few hours

Mature

10-9m nano space model

scanning microscope

image

Integration

-10 -9 -8 -7 -6 -50.00

0.05

0.10

0.15

0.20

28days7days

3days

1day

dV/d

lnr

log(r[m])

Capillary pore

Gel pore

r c

S dV/d log r

log r Vapor Transport

Liquid Transport

( ) ( )[ ][ ]K D S K h Mh RTV v o l=

2 5

1.

K rdVLl

rc=

2

0

2

50

Knudsen diffusion factor

History dependent liquid viscosity

Model assumptions micro-pores

gel

10-9m10-6m space structures 10-9m10-6m pore moisture state and motion

( ) ( ){ } 0,, =

hydl

l QTPPdivt

S J

10-6m10-3m scale potential flux term sink term

F= concrete composite

section

Integration

-10 -9 -8 -7 -6 -50.00

0.05

0.10

0.15

0.20

28days7days

3days

1day

dV/d

lnr

log(r[m])

Capillary pore

Gel pore

r c

S dV/d log r

log r Vapor Transport

Liquid Transport

( ) ( )[ ][ ]K D S K h Mh RTV v o l=

2 5

1.

K rdVLl

rc=

2

0

2

50

Knudsen diffusion factor

History dependent liquid viscosity

Model assumptions micro-pores

gel

10-9m 10-6m space structures 10-9m 10-6m pore moisture state and motion

Inner hydrate Outer hydrate Interlayer 2.8 thick

Gel pore II (1.6nm~) Pore among gel grain

Gel pore I (~1.6nm) Pore inside gel grain

Capillary pore Free space for hydrate

Unhydrated cement

Hydrate product (C-S-H grain)

Low hydration

After few hours

Mature

10-9m nano space model

scanning microscope

image

Integration

Time

Solidifying cluster of cement paste

Time

Solidifying cluster of cement paste

Micro-pores

Seepage of water

Micro-pores

Seepage of water 10-9m10-6m cement + moisture system

Time

Solidifying cluster of cement paste

Time

Solidifying cluster of cement paste

Micro-pores

Seepage of water

Micro-pores

Seepage of water 10-9m10-6m cement + moisture binder system

= ,,,

+ + = 0

10-6m10-3m stress gradient gravity acceeration term

Cement Paste

Vag Aggregate

Vcp

Integration

( ) ( ){ } 0,, =

hydl

l QTPPdivt

S J

10-6m10-3m scale potential flux term sink term

F= concrete composite

section

Integration

F(x,y,z) 1(x,y,z)dv = 0 F(x,y,z) 2(x,y,z)dv = 0 ... . ... F(x,y,z) (x,y,z)dv = 0

10-3 10-0m scale integral over the structural element

Weighted residual Function method

p =

+

3

=1

/

concrete composite section

Integration

(x,y,z) 1(x,y,z)dv = 0 (x,y,z) 2(x,y,z)dv = 0 ... . ... (x,y,z) (x,y,z)dv = 0

10-3 10-0m scale integral over the structural element with crack stress transfer

= ,,,

+ + = 0

10-6m10-3m stress gradient gravity acceeration term

=F

p =

+

3

=1

/

F 1(x,y,z)dv=0 F 2(x,y,z)dv=0 ... . F (x,y,z)dv=0

Cracked concrete

RC

Reinforcement

Local response

Mean stress of steel

Mean strain of steel

Averaged response ofsteel in concrete

Mean stressYield level

Crack locationMean strain

Local strain of steel

Local stress of steel

Average tensile strain

Crack widthCom

p. st

reng

th

redu

ction

1.0

Shear slip along a crack

Shea

r stre

ss

trans

ferre

d

Mean shear strain

Shea

r stre

ss

trans

ferre

d

Mean normal strain in x-dir.

Com

p.

stren

gth

redu

ction 1.0

Comp. strain

Crack location

Local strain of concrete

Mean stress Damage zone

LOCAL RESPONSE MEAN RESPONSEMulti-system

Com

p.

stren

gth

Integration= assembly of elements over 10+1~+2 m

coupling

Nonlinear dynamic structural analysis

() 1(x,y,z)dv=0 () 2(x,y,z)dv=0 ... ... () (x,y,z)dv=0

weak coupling

Seismic full 3D analysis : disp. At the 2nd floor

Magnification of displacement=5

X

Z

Y

In consideration of drying

Z experiment analysis

Effect of drying shrinkage on seismic performance

Ducom-COM3 link analysis

E-defense initial shrinkage cracking

3nd floor displacement

[mm mm]

10% 25%

50%

100%

~28 days sealed

7~28 days drying

Cracking and Drying (weak coupling): Experiment by Kim and Baant 1987 Baant et al. 1987 carried out experiment on the effect of cracking on diffusivity of concrete.

X-direction strain contour

Background

Role keeping lifelines underground

Research objectShallow underground RC culvert

Status of development

Many RC culverts constructed in urban areas

Deflection excess 3~4times of prediction

0

5

10

15

20

25

30N

umbe

r of c

rack

s

Crack width(mm)

Crack condition 30 years15 years

-15

-12

-9

-6

-3

0

-1500 -1000 -500 0 500 1000 1500

Dis

plac

emen

t(mm

)

Distance from center(mm)

Deflection shape of top slab (30years after completion)

Expected in design

Measured

Unknown cause deformation Future behavior is concerned about

Top slab350

400

3900

3200350 350

White line: chalked cracks

Actual crack picture mm

After a few decades, Long-term excessive deformations at the top slab are reported

Gas

Water supply

sewer Cable

Electric Wire

0

200

400

600

800

1000

1200

0.01 0.1 1 10 100 1000 10000

Measured

-15

-12

-9

-6

-3

0

0.01 0.1 1 10 100 1000 10000 100000

Def

lect

ion(

mm

)

Elapsed time after curing(day)

soil settlement

Case II,III simply added

Deflection at the center of top slab

Measured

RH:60%

Drying shrinkage, creep

RH:99.99%

Surrounding soil settlement

DesignRH:99%RH:

99.99%

RH:99.99%

RH:99.99%

RH:60%

Soil settlement+ drying shrinkage,creep

RH:99%

Differences reflect each effects

Design

Soil settlement Dry

2D: Long-time excessive deformation analysis

RC

Backfilled sand

100 160

360

35

C.L Based on actual structure and material

data

640 4 Contrast cases Model mesh

27.4years

Analytical results considering interacting behavior of structures and soil and Drying shrinkage show that long-term excessive deformation.

Mid-span tension steel strain

Time (day)

Mid

-spa

n de

flect

ion(

mm

)

(27.4years)

Soil settlement

Dry + soil settlement

Design

Dry

It shows that soil pressure is the main factor effecting steel tension strain.

Analytical soil pressure could reflect the real soil pressure.

Destructive test: drilling and scanning inside

Scan inside Core part

Scan photos

shear path of inclined crack

shear crack roughness level>flexure crack roughness

Crack

Coarse aggregate

Relative deformation

Steel rebar

Crack

Relative deformation

Crack

Coarse aggregate

Flat Opening

Steel rebar

Crack

Shear crack

Flexure crack

Hau

nch

Light H

aunc

h

(2)Use light to check the shadow

1-2mm raised

flexure

Punching failure after repetition of moving traffics

Life-Cycle Assessment and Inspection Data Assimilation for Concrete Bridge Deck Management

In design: fatigue life prediction In maintenance: remaining fatigue life with and without damage

strong coupling

Seismic Fatigue Numbers of cycles, strain levels, reversed/single sided cyclic

106-107 cycles, lower stress level 10-20 cycles, much high strain level single sided, 10-50 years reversed cyclic, 10-60 sec

FATIGUE EARTHQUAKE

Extended to High cycle Fatigue Simulation In the case of normal RC beams without any web reinforcement

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7

Vc/

Vco

log N

FE analysis

maxmin /

log)1(*036.0log

VVr

NrrVV

co

c

=

=

100cm

240cm

-0.005

-0.004

-0.003

-0.002

-0.001

0

0 5000 10000 15000 20000

time integration : t

logarithmic time integration : t (log t)

evolution term: dK=Fdt + Gd Ftd(logt)+ Gd

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8

Number of cycles and passages (log N)

Nor

mal

ized

ampl

itude

fixed point cyclic shear by FE analysis

Cyclic moving point shear by FE analysis

moving experiment by Matsui, et al. Perdikalis, et al. fixed pulsating by Perdikalis, et al.

Moving load 2~3 order reduced life stagnant water 1~2 order

Dry experimental results

Submerged experimental results

103 104 105 106 107

0.2

0.4

0.6

0

S-P/

Po

Cycle

Aggregation on Highway bridge deck

Aggregation (erosion) of concrete on bridge deck slab

East Nippon Expressway Co., Ltd

East Nippon Expressway Co., Ltd

VTR (Inspection)

Wheel loading test of RC slab specimen

Nihon University

CL Nihon University

Sawn specimen after loading test

Aggregation lead the failure of specimen

Erosion (disintegration) at the top surface of the slab

(Yokoyama et al. 2012)

Driving action of Erosion (disintegration, freeze-thaw)

Opening

Negative pressure

Closure

Positive pressure

Time (sec)

Pres

sure

(MPa

)

Erosion at the top surface of the slab

N=1 N=1000 N=30000

Dry Fatigue

Moist As above and Water compression and Reduction of Shear Transfer

Submerged As above and Erosion

Influence of water

Influence of erosion

OHnSiOONaNaOHnSiO 2222 2 ++

OmHnSiOONaOmHnSiOONa 222222 +

Gel production

Anisotropy of gel as a part of solid

ij = ij + ij li p li ; unit vector normal to crack plane

Adsorption of gel into micro-pores

0.0

Uniaxial confinement test

Beam model Mockup of footing

Confined expansion of ASR

Cracking along main bars Cracking at corners

Cracking along ties

XX[] YY[]

DuCOM-COM3 ASR reaction and expansion modeling verified

Axial expansion (exp) Axial expansion (analysis)

10cm10cm40cm prism

10cm18cm170cm

Cracking along steel bar

Confined by plates

Space-discretization 1/4

30cm45cm60cm

YY

ZZ

D13

D6

D10 Cracking according to the rebar arrangement

0 1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600 Experiment S2-C2 ; Analysis S2-C2 Experiment S2-C3 ; Analysis S2-C3 Experiment S2-C4 ; Analysis S2-C4 Experiment S2-C5 ; Analysis S2-C5

Stra

in, M

icron

Corrosion %

S2-C5 S2-C4

S2-C3

0 1 2 3 4 5 6 7 8 9 10-5.0-2.50.02.55.07.5

10.012.515.017.5

Inte

rface

def

orm

atio

n (

m)

Time (days)

Node_1 Node_2 Node_3 Node_4 Node_5 Node_6 Node_7 Node_8

DuCOM-COM3 Corrosion and expansion modeling verified

Experiment by Micheal et al. 2013 Experiment by Oh et al. 2008

0

1

2

3

1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 Equivalent repeated cycles

Deflection for

live load

(m

m)

Corroded bridge decks in lab. by Prof. Iwaki of Nihon Univ.

0.1

1

1.E+05 1.E+06 1.E+07 1.E+08

(P/Psx)

S-N

(1)

(2)

Equivalent number of cycle

Nor

mal

ized

shea

r for

ce

strong coupling

a)37800 b)278000

a)112 b)2760

Corroded bridge decks by analysis (Iwaki, Tsuchiya, Maekawa) Data assimilation in terms of corrosion degree

0 5 10 15 20

0 5 10 15

Corrosion rate (%)

Ion concentration (kg/m3)

Main ref

Distribution ref

Chloride concentration

Defle

ctio

n (m

m)

strong coupling

0

0.5

1

1.5

2

2.5

3

1.E+00 1.E+02 1.E+04 1.E+06 1.E+08

m

m)

Wheel type moving Loads by Prof. Iwaki, Nihon University Li

ve lo

ad d

efle

ctio

n (m

m)

Number of load cycle

No reactive aggregate

ASR + water

ASR

No acceleration

0

1000

2000

3000

4000

5000

6000

0 50 100 150 200

()

()

- - -

- - -Expansion in each axis

Vertical : 3000-5000

ASR

ASR + Water

No ASR

Fatigue analysis of ASR damaged decks (ASR+Force+water)

1800 of free expansion

FABriS software (2015 version) based on DuCOM-COM3 Cracks, water, NDT data, ambient states future life (fatigue failure)

Graphics switch

Crack information is converted to digit dataset.

Digitalized crack location and the width can be a part of database for maintenance of RC decks

Pseudo-Cracking Method

Crack maps by inspection Converted field of Pseudo-cracking strain

Conversion of current cracking to strain field

Dry No water in crack

Wet With water in crack

Influence of water (Analysis of moving load)

The influence of water

Fatigue life is reduced by 2-3 order under the influence of water. We cannot describe the cave-in of the strengthened slab.

RC Slab Load : 160kN

It has sufficient fatigue life at the design load level

Re-deterioration of Strengthened Slabs (Debonding, Cave-in)

Steel Plate Bonding Method Steel plate bonding method has been

applied in numerous bridges. Re-deterioration of strengthened slabs has

been reported. Neither experiments nor analysis have

systematically been made concerning the re-deterioration mechanism.

Source : http://www.nisshin-steel.co.jp/

Make clear the process of re-deterioration and residual life

S-N curve of corrosion of the strengthened slab

Case Corrosion Condition

Dry 0% Dry

Wet 0% Wet

Corr 50mg 1.60% Dry

Corr 20mg 0.64% Dry

Effects of corrosion

Numerical analysis showed fatigue life deteriorated because of corrosion of the strengthened slab.

Corrosion occur, rebar expand -> Concrete failed in layers -> Slab turned into a built-up beam -> Fatigue life deteriorated.

Additional beam

Steel plate bonded

S-N curve of strengthened damaged decks -Damaged concrete is not removed-

Overlaid upper face

Overlaid bottom face

S-N curve of strengthened damaged decks -Damaged concrete is not removed-

Remaining fatigue life assessment of existing RC bridge decks coupled with multi-scale platform

Combination of site inspection data and simulation platform M

ax. s

tress

/Com

p.S

treng

th

Log N

specified S-N diagram for design

0.01Hzanalysis rate ofloading = 1.0Hz

250

300

Compressive Strain

Compressive Stress (MPa)30

20

10

0.001 0.002 0.003

computational platform users

Pseudo-cracking method

Clear output S-N diagrams

site inspection simple measurement

Knowledge of engineers

Advice etc.

Compile & link

Knowledge of engineers

Thank you for your kind attention.

U-Tokyo 2015